Introduction

Most migration studies heavily physiological, while our aim with this is more functional (traits-based). Macroecological perspective on seasonal flux of animal movement (different from tracking studies), allowing cross-species comparisons of broad-scale strategies in pace and geography of annual cycle stages.

We also have certain species whose entire global population winters in India (e.g., Blyth’s Reed Warbler, Greenish Warbler). This is a good opportunity to gain understandings of global ecological (and conservation) significance.

Questions

  1. Cross-species comparisons:
    1. Does winter arrival/departure timing depend on the species’s wintering latitude?
    2. Does winter migration synchronicity depend on the species’s wintering latitude?
    3. Do species migrating later in season tend to migrate more synchronously?
    4. Is winter arrival/departure timing changing over the years (climate change)?
      • As a final section, if relevant and feasible (low data, quantile method might fail.).
      • Or, instead can maybe try to correlate with temperature gradient across latitudes to speculate.
  2. Within-species comparisons:
    1. Do species follow same synchronicity strategy for arrival and departure? (Symmetricity, see Winger et al. (2024))
      1. Which do, and which don’t (what determines this)?
    2. Is synchronicity more likely/common in arrival than in departure or vice-versa?
      • Many species have narrower window in spring than in fall (Winger et al. 2024 for references)
      • In India (maybe unique) we have monsoon, so most species probably spend longer coming down due to availability of food in post-monsoon

Northwest vs Himalayan routes

Metrics:

  • Migration timing:
    • True arrival/departure, not absolute (stragglers)
    • Synchronicity
  • Wintering latitude:
    • Minimum
    • Median
    • Extent/breadth/range

Exploration (methods)

For high-res versions of images, go here.

Investigating arrival and departure timings & synchronicity

After all our selection and filtering criteria for wintering species of interest (giving 90 species), and after filtering data for each species to its wintering latitudinal range (removing latitudes where not purely wintering), we now start the analysis.

Using quantiles (assuming 95%), we determine “true” arrival and departure dates for each species per latitude. For a preliminary visualisation of patterns across species, we visualise this latitudinal trend of arrival (blue) & departure (red) times for all species:

True arrival and departure timings of our wintering species, using the quantile method.

Figure 1: True arrival and departure timings of our wintering species, using the quantile method.

True arrival and departure timings of our wintering species, using the quantile method.

Figure 2: True arrival and departure timings of our wintering species, using the quantile method.

We now calculate metrics for migration timings, such as first northern/southern arrival & departure, and synchronicity which is our primary metric of interest. We describe synchronicity using two (presumably) orthogonal angles: slope (quickness of migration) and tightness (uniformity) across latitudes. (Correlation R^2 cannot be used for the measure of tightness, since for high slope values, R2 becomes low.)

Here are the synchronicity measures (SYNC.SLOPE & SYNC.TIGHT) for a set of illustrative species, followed by updated plots for the same species.

## # A tibble: 50 × 6
##    COMMON.NAME               DATE.TYPE   SLOPE    SE SYNC.SLOPE SYNC.TIGHT
##    <chr>                     <fct>       <dbl> <dbl>      <dbl>      <dbl>
##  1 Cinereous Vulture         DEP        6.21   0.921  -1.60         0.0827
##  2 Bar-tailed Godwit         DEP        3.89   2.60   -1.19        -0.956 
##  3 Brown-breasted Flycatcher DEP        2.47   0.479  -0.795        0.737 
##  4 Black Redstart            DEP        2.21   0.292  -0.696        1.23  
##  5 Blyth's Reed Warbler      DEP        1.86   0.213  -0.548        1.55  
##  6 Red-breasted Flycatcher   DEP        1.53   0.312  -0.373        1.16  
##  7 Lesser Whitethroat        DEP        1.50   0.462  -0.361        0.771 
##  8 Common Chiffchaff         DEP        1.46   0.410  -0.332        0.891 
##  9 Siberian Stonechat        DEP        1.39   0.246  -0.293        1.40  
## 10 Bar-headed Goose          DEP        1.26   0.283  -0.203        1.26  
## 11 Taiga Flycatcher          DEP        0.988  0.300   0.00665      1.21  
## 12 Eurasian Wigeon           DEP        0.795  0.344   0.197        1.07  
## 13 Brown-headed Gull         DEP       -0.766  0.472   0.229        0.750 
## 14 Brown Shrike              DEP        0.519  0.282   0.570        1.27  
## 15 Tufted Duck               DEP        0.511  0.447   0.584        0.806 
## 16 Spotted Redshank          DEP        0.504  0.327   0.595        1.12  
## 17 Greenish Warbler          DEP       -0.459  0.362   0.677        1.02  
## 18 Gray Wagtail              DEP        0.425  0.253   0.745        1.38  
## 19 Green Warbler             DEP        0.363  0.467   0.883        0.762 
## 20 Common Buzzard            DEP       -0.272  0.880   1.13         0.128 
## 21 Greater Spotted Eagle     DEP        0.245  0.254   1.23         1.37  
## 22 Sykes's Warbler           DEP        0.147  0.847   1.67         0.166 
## 23 Western Yellow Wagtail    DEP        0.0612 0.241   2.44         1.42  
## 24 Booted Eagle              DEP       -0.0444 0.250   2.72         1.39  
## 25 Pallid Harrier            DEP        0.0227 0.334   3.31         1.10  
## 26 Blyth's Reed Warbler      ARR       -3.33   0.459  -1.06         0.778 
## 27 Cinereous Vulture         ARR       -2.39   2.38   -0.766       -0.866 
## 28 Green Warbler             ARR       -1.78   0.270  -0.510        1.31  
## 29 Brown-breasted Flycatcher ARR       -1.78   1.02   -0.506       -0.0229
## 30 Western Yellow Wagtail    ARR       -1.73   0.204  -0.481        1.59  
## 31 Pallid Harrier            ARR       -1.62   0.240  -0.423        1.43  
## 32 Sykes's Warbler           ARR       -1.51   0.984  -0.362        0.0157
## 33 Eurasian Wigeon           ARR       -1.35   0.272  -0.266        1.30  
## 34 Common Chiffchaff         ARR       -1.22   0.440  -0.176        0.821 
## 35 Brown-headed Gull         ARR       -1.04   0.533  -0.0368       0.630 
## 36 Bar-tailed Godwit         ARR       -0.997  0.958  -0.000733     0.0428
## 37 Greenish Warbler          ARR       -0.980  0.280   0.0143       1.27  
## 38 Booted Eagle              ARR       -0.976  0.209   0.0177       1.57  
## 39 Brown Shrike              ARR       -0.732  0.160   0.270        1.83  
## 40 Taiga Flycatcher          ARR       -0.722  0.250   0.281        1.39  
## 41 Siberian Stonechat        ARR       -0.705  0.182   0.302        1.70  
## 42 Tufted Duck               ARR       -0.700  0.527   0.308        0.640 
## 43 Red-breasted Flycatcher   ARR       -0.642  0.248   0.384        1.39  
## 44 Lesser Whitethroat        ARR       -0.610  0.255   0.429        1.36  
## 45 Spotted Redshank          ARR        0.552  1.02    0.516       -0.0168
## 46 Common Buzzard            ARR        0.480  0.335   0.637        1.09  
## 47 Black Redstart            ARR       -0.409  0.172   0.779        1.76  
## 48 Gray Wagtail              ARR        0.342  0.209   0.934        1.57  
## 49 Bar-headed Goose          ARR       -0.129  0.146   1.79         1.92  
## 50 Greater Spotted Eagle     ARR        0.0515 0.332   2.59         1.10
Set of illustrative species arranged in order of synchronicity of arrival/departure.

Figure 3: Set of illustrative species arranged in order of synchronicity of arrival/departure.

Set of illustrative species arranged in order of synchronicity of arrival/departure.

Figure 4: Set of illustrative species arranged in order of synchronicity of arrival/departure.

All our species can be visualised as occupying a 2-D space governed by the two measures of synchronicity. Based on their occupancy of this space, we can classify their overall synchronicity.

2D space of synchronicity measures of our species.

Figure 5: 2D space of synchronicity measures of our species.

Now will try to combine the two variables into a single index of synchronicity. Relative weights are obtained from PCA of the two variables, and the index (SYNC.IND) is a linear combination of the two. New values and updated graphs below.

## # A tibble: 50 × 5
##    COMMON.NAME               DATE.TYPE SYNC.SLOPE SYNC.TIGHT SYNC.IND
##    <chr>                     <fct>          <dbl>      <dbl>    <dbl>
##  1 Bar-tailed Godwit         DEP        -1.19        -0.956  -1.12   
##  2 Cinereous Vulture         DEP        -1.60         0.0827 -1.08   
##  3 Brown-breasted Flycatcher DEP        -0.795        0.737  -0.320  
##  4 Black Redstart            DEP        -0.696        1.23   -0.0982 
##  5 Lesser Whitethroat        DEP        -0.361        0.771  -0.00962
##  6 Common Chiffchaff         DEP        -0.332        0.891   0.0472 
##  7 Blyth's Reed Warbler      DEP        -0.548        1.55    0.102  
##  8 Red-breasted Flycatcher   DEP        -0.373        1.16    0.103  
##  9 Siberian Stonechat        DEP        -0.293        1.40    0.233  
## 10 Bar-headed Goose          DEP        -0.203        1.26    0.252  
## 11 Taiga Flycatcher          DEP         0.00665      1.21    0.378  
## 12 Brown-headed Gull         DEP         0.229        0.750   0.391  
## 13 Eurasian Wigeon           DEP         0.197        1.07    0.466  
## 14 Tufted Duck               DEP         0.584        0.806   0.653  
## 15 Spotted Redshank          DEP         0.595        1.12    0.757  
## 16 Greenish Warbler          DEP         0.677        1.02    0.782  
## 17 Brown Shrike              DEP         0.570        1.27    0.786  
## 18 Common Buzzard            DEP         1.13         0.128   0.822  
## 19 Green Warbler             DEP         0.883        0.762   0.846  
## 20 Gray Wagtail              DEP         0.745        1.38    0.940  
## 21 Sykes's Warbler           DEP         1.67         0.166   1.21   
## 22 Greater Spotted Eagle     DEP         1.23         1.37    1.27   
## 23 Western Yellow Wagtail    DEP         2.44         1.42    2.13   
## 24 Booted Eagle              DEP         2.72         1.39    2.31   
## 25 Pallid Harrier            DEP         3.31         1.10    2.62   
## 26 Cinereous Vulture         ARR        -0.766       -0.866  -0.797  
## 27 Blyth's Reed Warbler      ARR        -1.06         0.778  -0.487  
## 28 Brown-breasted Flycatcher ARR        -0.506       -0.0229 -0.357  
## 29 Sykes's Warbler           ARR        -0.362        0.0157 -0.245  
## 30 Bar-tailed Godwit         ARR        -0.000733     0.0428  0.0127 
## 31 Green Warbler             ARR        -0.510        1.31    0.0545 
## 32 Common Chiffchaff         ARR        -0.176        0.821   0.133  
## 33 Pallid Harrier            ARR        -0.423        1.43    0.151  
## 34 Western Yellow Wagtail    ARR        -0.481        1.59    0.160  
## 35 Brown-headed Gull         ARR        -0.0368       0.630   0.170  
## 36 Eurasian Wigeon           ARR        -0.266        1.30    0.220  
## 37 Spotted Redshank          ARR         0.516       -0.0168  0.351  
## 38 Greenish Warbler          ARR         0.0143       1.27    0.405  
## 39 Tufted Duck               ARR         0.308        0.640   0.411  
## 40 Booted Eagle              ARR         0.0177       1.57    0.498  
## 41 Taiga Flycatcher          ARR         0.281        1.39    0.624  
## 42 Red-breasted Flycatcher   ARR         0.384        1.39    0.697  
## 43 Lesser Whitethroat        ARR         0.429        1.36    0.719  
## 44 Siberian Stonechat        ARR         0.302        1.70    0.736  
## 45 Brown Shrike              ARR         0.270        1.83    0.754  
## 46 Common Buzzard            ARR         0.637        1.09    0.779  
## 47 Black Redstart            ARR         0.779        1.76    1.08   
## 48 Gray Wagtail              ARR         0.934        1.57    1.13   
## 49 Bar-headed Goose          ARR         1.79         1.92    1.83   
## 50 Greater Spotted Eagle     ARR         2.59         1.10    2.13
Species arranged in order of combination of two synchronicity measures.

Figure 6: Species arranged in order of combination of two synchronicity measures.

Species arranged in order of combination of two synchronicity measures.

Figure 7: Species arranged in order of combination of two synchronicity measures.

Clearly, there is still some finetuning to be done with the “quickness” metric, i.e., derived from slope. For the most synchronous species with little difference between them, the values are drastically different. Also need to figure out how to appropriately weight the two so that high togetherness is prioritised.

Further try ordinations to understand what factors (wintering, migrating) determine synchronicity of species.

Finalise synchronicity

On discussing with AV, we realised that the second aspect, “tightness” is better viewed as noise rather than information. Even if it appears to have ecological meaning, this is only true for high tightness values and here the information is mostly just from the first metric. So, instead of trying to combine the two aspects, better to ignore species with tightness lower than some threshold value. Consider that low tightness can either be just noise in data, or lack of a strong north-south migration signal in the species, and we can’t tease apart the two (and not of interest in this study; though might still be an orthogonal aspect of synchronicity). So, changes applied:

  • Set threshold for variability (tightness) along slope, exclude species above this from our main regression tests with latitude
  • With all species (including those excluded above), we divide synchronicity into N bins (think X axis of Fig. 5) and within each bin show how variability (signal) can range from low to high. e.g., highly staggered species can range from BRW (very strong migration signal) to CiVu (less strong signal); very synchronous species can range from BHGo to SpRedshank.
  • So now our measure of synchronicity is much simplified: there is only one metric, and that too can be simply the slope from the LM (without any transformations).
    • LM seems the best bet here; I did try GLM but the slope there is not the information we want
    • Also, LM estimates with and without scaling the DAY.MY to start from 0 (for each species and arrival/departure combo) were the same, so leave it unscaled. See below.
## # A tibble: 5 × 8
##   COMMON.NAME    DATE.TYPE LM.SLOPE LM.SE SCALED.LM.SLOPE SCALED.LM.SE GLM.SLOPE
##   <chr>          <fct>        <dbl> <dbl>           <dbl>        <dbl>     <dbl>
## 1 Black-capped … ARR        -2.11    2.87         -2.11           2.87     0.979
## 2 Black-naped O… ARR         2.78    1.47          2.78           1.47     1.03 
## 3 Black-throate… ARR        -3.67    1.39         -3.67           1.39     0.876
## 4 Common Pochard ARR         0.0714  1.06          0.0714         1.06     1.00 
## 5 Eurasian Grif… ARR        -0.514   2.05         -0.514          2.05     0.942
## # ℹ 1 more variable: GLM.SE <dbl>

Arranging in order of new synchronicity index (slope of LM):

## # A tibble: 50 × 4
##    COMMON.NAME               DATE.TYPE SYNC.IND    SE
##    <chr>                     <fct>        <dbl> <dbl>
##  1 Brown-headed Gull         DEP        -0.766  0.472
##  2 Greenish Warbler          DEP        -0.459  0.362
##  3 Common Buzzard            DEP        -0.272  0.880
##  4 Booted Eagle              DEP        -0.0444 0.250
##  5 Pallid Harrier            DEP         0.0227 0.334
##  6 Western Yellow Wagtail    DEP         0.0612 0.241
##  7 Sykes's Warbler           DEP         0.147  0.847
##  8 Greater Spotted Eagle     DEP         0.245  0.254
##  9 Green Warbler             DEP         0.363  0.467
## 10 Gray Wagtail              DEP         0.425  0.253
## 11 Spotted Redshank          DEP         0.504  0.327
## 12 Tufted Duck               DEP         0.511  0.447
## 13 Brown Shrike              DEP         0.519  0.282
## 14 Eurasian Wigeon           DEP         0.795  0.344
## 15 Taiga Flycatcher          DEP         0.988  0.300
## 16 Bar-headed Goose          DEP         1.26   0.283
## 17 Siberian Stonechat        DEP         1.39   0.246
## 18 Common Chiffchaff         DEP         1.46   0.410
## 19 Lesser Whitethroat        DEP         1.50   0.462
## 20 Red-breasted Flycatcher   DEP         1.53   0.312
## 21 Blyth's Reed Warbler      DEP         1.86   0.213
## 22 Black Redstart            DEP         2.21   0.292
## 23 Brown-breasted Flycatcher DEP         2.47   0.479
## 24 Bar-tailed Godwit         DEP         3.89   2.60 
## 25 Cinereous Vulture         DEP         6.21   0.921
## 26 Blyth's Reed Warbler      ARR        -3.33   0.459
## 27 Cinereous Vulture         ARR        -2.39   2.38 
## 28 Green Warbler             ARR        -1.78   0.270
## 29 Brown-breasted Flycatcher ARR        -1.78   1.02 
## 30 Western Yellow Wagtail    ARR        -1.73   0.204
## 31 Pallid Harrier            ARR        -1.62   0.240
## 32 Sykes's Warbler           ARR        -1.51   0.984
## 33 Eurasian Wigeon           ARR        -1.35   0.272
## 34 Common Chiffchaff         ARR        -1.22   0.440
## 35 Brown-headed Gull         ARR        -1.04   0.533
## 36 Bar-tailed Godwit         ARR        -0.997  0.958
## 37 Greenish Warbler          ARR        -0.980  0.280
## 38 Booted Eagle              ARR        -0.976  0.209
## 39 Brown Shrike              ARR        -0.732  0.160
## 40 Taiga Flycatcher          ARR        -0.722  0.250
## 41 Siberian Stonechat        ARR        -0.705  0.182
## 42 Tufted Duck               ARR        -0.700  0.527
## 43 Red-breasted Flycatcher   ARR        -0.642  0.248
## 44 Lesser Whitethroat        ARR        -0.610  0.255
## 45 Black Redstart            ARR        -0.409  0.172
## 46 Bar-headed Goose          ARR        -0.129  0.146
## 47 Greater Spotted Eagle     ARR         0.0515 0.332
## 48 Gray Wagtail              ARR         0.342  0.209
## 49 Common Buzzard            ARR         0.480  0.335
## 50 Spotted Redshank          ARR         0.552  1.02
Species arranged in order of synchronicity (slope).

Figure 8: Species arranged in order of synchronicity (slope).

Species arranged in order of synchronicity (slope).

Figure 9: Species arranged in order of synchronicity (slope).

Determining threshold cutoff for variability (tightness)

This is not very straightforward. Here is a summary of some select species and various measures of theirs (R-squared, residual standard error, degrees of freedom, F statistic, root mean square error, mean absolute error, coefficient of variation).

## # A tibble: 50 × 11
##    COMMON.NAME   DATE.TYPE   SLOPE    SE      R2   RSE    DF  F.STAT  RMSE   MAE
##    <chr>         <fct>       <dbl> <dbl>   <dbl> <dbl> <int>   <dbl> <dbl> <dbl>
##  1 Bar-headed G… DEP        1.26   0.283 4.73e-1  9.58    22 1.97e+1  9.17  7.31
##  2 Bar-headed G… ARR       -0.129  0.146 3.41e-2  4.95    22 7.77e-1  4.74  3.83
##  3 Bar-tailed G… DEP        3.89   2.60  2.71e-1 22.6      6 2.24e+0 19.6  14.7 
##  4 Bar-tailed G… ARR       -0.997  0.958 1.53e-1  8.33     6 1.08e+0  7.21  5.37
##  5 Black Redsta… DEP        2.21   0.292 7.82e-1  6.72    16 5.73e+1  6.34  5.27
##  6 Black Redsta… ARR       -0.409  0.172 2.61e-1  3.96    16 5.65e+0  3.74  2.90
##  7 Blyth's Reed… DEP        1.86   0.213 7.78e-1  7.21    22 7.70e+1  6.90  5.77
##  8 Blyth's Reed… ARR       -3.33   0.459 7.05e-1 15.6     22 5.25e+1 14.9  11.0 
##  9 Booted Eagle  DEP       -0.0444 0.250 1.74e-3  6.45    18 3.14e-2  6.12  4.95
## 10 Booted Eagle  ARR       -0.976  0.209 5.48e-1  5.38    18 2.19e+1  5.11  3.69
## 11 Brown Shrike  DEP        0.519  0.282 1.34e-1  9.55    22 3.40e+0  9.14  6.49
## 12 Brown Shrike  ARR       -0.732  0.160 4.88e-1  5.42    22 2.10e+1  5.19  3.77
## 13 Brown-breast… DEP        2.47   0.479 7.08e-1  7.30    11 2.67e+1  6.72  5.03
## 14 Brown-breast… ARR       -1.78   1.02  2.15e-1 15.6     11 3.02e+0 14.4   8.60
## 15 Brown-headed… DEP       -0.766  0.472 1.41e-1 13.2     16 2.63e+0 12.5   9.69
## 16 Brown-headed… ARR       -1.04   0.533 1.92e-1 14.9     16 3.80e+0 14.1  10.6 
## 17 Cinereous Vu… DEP        6.21   0.921 8.35e-1 10.5      9 4.55e+1  9.48  8.07
## 18 Cinereous Vu… ARR       -2.39   2.38  1.01e-1 27.1      9 1.01e+0 24.5  17.6 
## 19 Common Buzza… DEP       -0.272  0.880 6.79e-3 21.2     14 9.58e-2 19.9  14.1 
## 20 Common Buzza… ARR        0.480  0.335 1.28e-1  8.08    14 2.06e+0  7.56  5.58
## 21 Common Chiff… DEP        1.46   0.410 4.57e-1  8.28    15 1.26e+1  7.78  6.10
## 22 Common Chiff… ARR       -1.22   0.440 3.38e-1  8.88    15 7.67e+0  8.34  6.35
## 23 Eurasian Wig… DEP        0.795  0.344 1.95e-1 12.4     22 5.33e+0 11.9   8.88
## 24 Eurasian Wig… ARR       -1.35   0.272 5.27e-1  9.81    22 2.45e+1  9.39  7.30
## 25 Gray Wagtail  DEP        0.425  0.253 1.36e-1  6.52    18 2.82e+0  6.18  5.05
## 26 Gray Wagtail  ARR        0.342  0.209 1.30e-1  5.38    18 2.69e+0  5.10  4.07
## 27 Greater Spot… DEP        0.245  0.254 3.87e-2  9.16    23 9.27e-1  8.79  6.80
## 28 Greater Spot… ARR        0.0515 0.332 1.04e-3 12.0     23 2.40e-2 11.5   8.01
## 29 Green Warbler DEP        0.363  0.467 3.87e-2  9.43    15 6.04e-1  8.86  7.02
## 30 Green Warbler ARR       -1.78   0.270 7.45e-1  5.44    15 4.38e+1  5.11  3.92
## 31 Greenish War… DEP       -0.459  0.362 7.45e-2 10.8     20 1.61e+0 10.3   8.83
## 32 Greenish War… ARR       -0.980  0.280 3.80e-1  8.32    20 1.23e+1  7.94  6.29
## 33 Lesser White… DEP        1.50   0.462 3.35e-1 14.7     21 1.06e+1 14.1  10.9 
## 34 Lesser White… ARR       -0.610  0.255 2.13e-1  8.13    21 5.70e+0  7.76  6.39
## 35 Pallid Harri… DEP        0.0227 0.334 2.56e-4  8.96    18 4.60e-3  8.50  7.00
## 36 Pallid Harri… ARR       -1.62   0.240 7.16e-1  6.43    18 4.53e+1  6.10  5.03
## 37 Red-breasted… DEP        1.53   0.312 5.45e-1  9.28    20 2.39e+1  8.85  6.69
## 38 Red-breasted… ARR       -0.642  0.248 2.50e-1  7.39    20 6.68e+0  7.05  6.05
## 39 Siberian Sto… DEP        1.39   0.246 6.67e-1  5.86    16 3.21e+1  5.52  4.50
## 40 Siberian Sto… ARR       -0.705  0.182 4.83e-1  4.35    16 1.49e+1  4.10  3.04
## 41 Spotted Reds… DEP        0.504  0.327 1.16e-1  9.96    18 2.37e+0  9.45  7.35
## 42 Spotted Reds… ARR        0.552  1.02  1.61e-2 30.9     18 2.94e-1 29.4  22.4 
## 43 Sykes's Warb… DEP        0.147  0.847 2.00e-3 18.5     15 3.01e-2 17.3  13.1 
## 44 Sykes's Warb… ARR       -1.51   0.984 1.35e-1 21.5     15 2.34e+0 20.2  17.3 
## 45 Taiga Flycat… DEP        0.988  0.300 3.64e-1  8.31    19 1.09e+1  7.91  5.59
## 46 Taiga Flycat… ARR       -0.722  0.250 3.05e-1  6.93    19 8.35e+0  6.60  5.46
## 47 Tufted Duck   DEP        0.511  0.447 9.13e-2  7.48    13 1.31e+0  6.96  6.28
## 48 Tufted Duck   ARR       -0.700  0.527 1.19e-1  8.82    13 1.76e+0  8.21  6.67
## 49 Western Yell… DEP        0.0612 0.241 2.93e-3  8.50    22 6.46e-2  8.14  6.13
## 50 Western Yell… ARR       -1.73   0.204 7.65e-1  7.22    22 7.15e+1  6.91  5.48
## # ℹ 1 more variable: CV <dbl>

RMSE, MAE, and RSE make the most sense. Using thresholds of 20, 20, and 25 respectively, here is a summary of our example species that passed or failed wrt ARRIVAL timings.

## # A tibble: 25 × 9
##    COMMON.NAME         SLOPE    SE   RSE  RMSE   MAE RSE.PASS RMSE.PASS MAE.PASS
##    <chr>               <dbl> <dbl> <dbl> <dbl> <dbl> <lgl>    <lgl>     <lgl>   
##  1 Bar-headed Goose  -0.129  0.146  4.95  4.74  3.83 TRUE     TRUE      TRUE    
##  2 Bar-tailed Godwit -0.997  0.958  8.33  7.21  5.37 TRUE     TRUE      TRUE    
##  3 Black Redstart    -0.409  0.172  3.96  3.74  2.90 TRUE     TRUE      TRUE    
##  4 Blyth's Reed War… -3.33   0.459 15.6  14.9  11.0  TRUE     TRUE      TRUE    
##  5 Booted Eagle      -0.976  0.209  5.38  5.11  3.69 TRUE     TRUE      TRUE    
##  6 Brown Shrike      -0.732  0.160  5.42  5.19  3.77 TRUE     TRUE      TRUE    
##  7 Brown-breasted F… -1.78   1.02  15.6  14.4   8.60 TRUE     TRUE      TRUE    
##  8 Brown-headed Gull -1.04   0.533 14.9  14.1  10.6  TRUE     TRUE      TRUE    
##  9 Cinereous Vulture -2.39   2.38  27.1  24.5  17.6  FALSE    FALSE     TRUE    
## 10 Common Buzzard     0.480  0.335  8.08  7.56  5.58 TRUE     TRUE      TRUE    
## 11 Common Chiffchaff -1.22   0.440  8.88  8.34  6.35 TRUE     TRUE      TRUE    
## 12 Eurasian Wigeon   -1.35   0.272  9.81  9.39  7.30 TRUE     TRUE      TRUE    
## 13 Gray Wagtail       0.342  0.209  5.38  5.10  4.07 TRUE     TRUE      TRUE    
## 14 Greater Spotted …  0.0515 0.332 12.0  11.5   8.01 TRUE     TRUE      TRUE    
## 15 Green Warbler     -1.78   0.270  5.44  5.11  3.92 TRUE     TRUE      TRUE    
## 16 Greenish Warbler  -0.980  0.280  8.32  7.94  6.29 TRUE     TRUE      TRUE    
## 17 Lesser Whitethro… -0.610  0.255  8.13  7.76  6.39 TRUE     TRUE      TRUE    
## 18 Pallid Harrier    -1.62   0.240  6.43  6.10  5.03 TRUE     TRUE      TRUE    
## 19 Red-breasted Fly… -0.642  0.248  7.39  7.05  6.05 TRUE     TRUE      TRUE    
## 20 Siberian Stonech… -0.705  0.182  4.35  4.10  3.04 TRUE     TRUE      TRUE    
## 21 Spotted Redshank   0.552  1.02  30.9  29.4  22.4  FALSE    FALSE     FALSE   
## 22 Sykes's Warbler   -1.51   0.984 21.5  20.2  17.3  TRUE     FALSE     TRUE    
## 23 Taiga Flycatcher  -0.722  0.250  6.93  6.60  5.46 TRUE     TRUE      TRUE    
## 24 Tufted Duck       -0.700  0.527  8.82  8.21  6.67 TRUE     TRUE      TRUE    
## 25 Western Yellow W… -1.73   0.204  7.22  6.91  5.48 TRUE     TRUE      TRUE
Comparisons of different measures of variability for arrival timings.

Figure 10: Comparisons of different measures of variability for arrival timings.

It is evident that RMSE is the most susceptible to single, large-deviance points pulling away the overall measure. It also seems that MAE might be the most appropriate for us: aside from Dunlin and Pied Harrier (which are treated similarly by all three), all other remove species have been clustered tightly and separated from the species we want to retain.

Let us check whether this is true for departure timings as well. Here, the best thresholds are 14, 10 and 15 respectively for RMSE, MAE and RSE.

## # A tibble: 25 × 9
##    COMMON.NAME         SLOPE    SE   RSE  RMSE   MAE RSE.PASS RMSE.PASS MAE.PASS
##    <chr>               <dbl> <dbl> <dbl> <dbl> <dbl> <lgl>    <lgl>     <lgl>   
##  1 Bar-headed Goose   1.26   0.283  9.58  9.17  7.31 TRUE     TRUE      TRUE    
##  2 Bar-tailed Godwit  3.89   2.60  22.6  19.6  14.7  FALSE    FALSE     FALSE   
##  3 Black Redstart     2.21   0.292  6.72  6.34  5.27 TRUE     TRUE      TRUE    
##  4 Blyth's Reed War…  1.86   0.213  7.21  6.90  5.77 TRUE     TRUE      TRUE    
##  5 Booted Eagle      -0.0444 0.250  6.45  6.12  4.95 TRUE     TRUE      TRUE    
##  6 Brown Shrike       0.519  0.282  9.55  9.14  6.49 TRUE     TRUE      TRUE    
##  7 Brown-breasted F…  2.47   0.479  7.30  6.72  5.03 TRUE     TRUE      TRUE    
##  8 Brown-headed Gull -0.766  0.472 13.2  12.5   9.69 TRUE     TRUE      TRUE    
##  9 Cinereous Vulture  6.21   0.921 10.5   9.48  8.07 TRUE     TRUE      TRUE    
## 10 Common Buzzard    -0.272  0.880 21.2  19.9  14.1  FALSE    FALSE     FALSE   
## 11 Common Chiffchaff  1.46   0.410  8.28  7.78  6.10 TRUE     TRUE      TRUE    
## 12 Eurasian Wigeon    0.795  0.344 12.4  11.9   8.88 TRUE     TRUE      TRUE    
## 13 Gray Wagtail       0.425  0.253  6.52  6.18  5.05 TRUE     TRUE      TRUE    
## 14 Greater Spotted …  0.245  0.254  9.16  8.79  6.80 TRUE     TRUE      TRUE    
## 15 Green Warbler      0.363  0.467  9.43  8.86  7.02 TRUE     TRUE      TRUE    
## 16 Greenish Warbler  -0.459  0.362 10.8  10.3   8.83 TRUE     TRUE      TRUE    
## 17 Lesser Whitethro…  1.50   0.462 14.7  14.1  10.9  TRUE     FALSE     FALSE   
## 18 Pallid Harrier     0.0227 0.334  8.96  8.50  7.00 TRUE     TRUE      TRUE    
## 19 Red-breasted Fly…  1.53   0.312  9.28  8.85  6.69 TRUE     TRUE      TRUE    
## 20 Siberian Stonech…  1.39   0.246  5.86  5.52  4.50 TRUE     TRUE      TRUE    
## 21 Spotted Redshank   0.504  0.327  9.96  9.45  7.35 TRUE     TRUE      TRUE    
## 22 Sykes's Warbler    0.147  0.847 18.5  17.3  13.1  FALSE    FALSE     FALSE   
## 23 Taiga Flycatcher   0.988  0.300  8.31  7.91  5.59 TRUE     TRUE      TRUE    
## 24 Tufted Duck        0.511  0.447  7.48  6.96  6.28 TRUE     TRUE      TRUE    
## 25 Western Yellow W…  0.0612 0.241  8.50  8.14  6.13 TRUE     TRUE      TRUE
Comparisons of different measures of variability for departure timings.

Figure 11: Comparisons of different measures of variability for departure timings.

RMSE seems like a poor option again. MAE is again decent, but this time RSE is also good. Need to see how values for species change with updated 2024 data.

The number of species that pass and fail each criterion are:

## # A tibble: 6 × 5
##   DATE.TYPE CRITERION  FAIL  PASS PASS.PROP
##   <fct>     <chr>     <int> <int>     <dbl>
## 1 DEP       MAE.PASS     35    55     0.611
## 2 DEP       RMSE.PASS    26    64     0.711
## 3 DEP       RSE.PASS     27    63     0.7  
## 4 ARR       MAE.PASS      7    83     0.922
## 5 ARR       RMSE.PASS    12    78     0.867
## 6 ARR       RSE.PASS      9    81     0.9

References

Åkesson, S., Ilieva, M., Karagicheva, J., Rakhimberdiev, E., Tomotani, B., & Helm, B., 2017. Timing avian long-distance migration: From internal clock mechanisms to global flights. Philosophical Transactions of the Royal Society B: Biological Sciences 372 (1734):20160252.
Gordo, O., Brotons, L., Ferrer, X., & Comas, P., 2005. Do changes in climate patterns in wintering areas affect the timing of the spring arrival of trans-Saharan migrant birds? Global Change Biology 11 (1):12–21.
Hagan, J. M., Lloyd-Evans, T. L., & Atwood, J. L., 1991. The Relationship between Latitude and the Timing of Spring Migration of North American Landbirds. Ornis Scandinavica (Scandinavian Journal of Ornithology) 22 (2):129–136.
Saino, N., Szép, T., Romano, M., Rubolini, D., Spina, F., & Møller, A. P., 2004. Ecological conditions during winter predict arrival date at the breeding quarters in a trans-Saharan migratory bird. Ecology Letters 7 (1):21–25.
Winger, B. M., Sorte, F. A. L., Hack, M. D., & Pegan, T. M., 2024. Evolutionary integration of the geography and pacing of the annual cycle in migratory birds.